The strong mixing and the selfdecomposability properties

TL;DR

This paper proves that normalized sums of strongly mixing, non-stationary random sequences converge to selfdecomposable distributions, expanding understanding of limit behaviors in dependent sequences.

Contribution

It demonstrates that only selfdecomposable distributions can arise as limits from normalized sums of strongly mixing, non-stationary sequences.

Findings

Limits are only selfdecomposable distributions.

Strong mixing is sufficient for selfdecomposability in limits.

Non-stationarity does not prevent convergence to selfdecomposable laws.

Abstract

It is proved that infinitesimal triangular arrays obtained from normalized partial sums of strongly mixing (but not necessarily stationary) random sequences, can produce as lilmits only selfdecomposable distributions.